What happened to 'new math'?

‘New math’ is remembered now as “a dismal mistake”, and has been called “one of the worst ideas of the 20th century”—but, to many of the brightest minds in education and mathematics, it seemed like a good idea at the time. So, where did ‘new math’ come from, and what went wrong? And sixty years later, what has it taught us about the nature of education reform?

Chapters:
0:00 Introduction
3:16 Chapter 1: Math After WWII
9:02 Chapter 2: New Math Dawns
18:20 Chapter 3: High School New Math
20:30 Chapter 4: Elementary School New Math
25:29 Chapter 5: The Fall of New Math
30:16 Chapter 6: After New Math
32:35 Epilogue: New Math's Legacy

[Maggie-trkd]

I was confronted with "new math" in junior high school about 1966/1967. I hated it and I could not understand it. My father, a brilliant chemical engineer, bought the new math textbook to keep at home (so I wouldn't have to keep bringing the textbook home from school) and sat with me for countless hours trying to help me with it. On assignments and tests we were supposed to show all of these logical steps to get to the solution. My father could show me how to work these problems in 2 or 3 steps but the teacher wanted 6-7 steps or more. My father could not understand why there was a need for all these steps. Once I knew how to work the problems in 2 or 3 steps and get all the answers correct, the teacher would still give me a low grade because I failed to show all of the steps despite correct answers. I remember feeling angry and crying with frustration many many nights. My father thought showing all these unneeded steps was ridiculous but he kept working with me until I could do it and make a good grade in the class at the end. My love for my father blossomed but I took a dim view of math after that. In high school, I took 3 years of algebra and a year of geometry after the new math was no longer taught. I even took math in college in case I would need it in my career. But, the joy of numbers was gone. In my opinion, new math was a terrible mistake and, for me, it left a scar.

[benjaminsmith]

Throughout all these decades, the military has been printing its own textbooks so cheaply that they can pretty much give them away, on a huge variety of subjects. At the same time, publishers sold textbooks to every public school at 100x markups, making meaningless changes along the way to force repeat purchases. This has nothing to do with math.

[maxxwellbeing]

In the seventies, my grade 3 teacher would teach us our times table, then teach us how to get the answers in long form, and then, she would give us sheets of math problems with the wrong answers. Or job was to find which answers were wrong and correct them. We scored the highest of any other class, all of use had marks in the 90s and she had a helping atmosphere where she put the kids with problems with the smart kids and the goal of all of us was to help each other. Best teacher ever.

[englishwithkaren]

Lol! I remember the psychology of first grade new math: feelings of abandonment as I raised my hand during entire math sessions, learning how to be secretive as I tore and stuffed into my desk all “new math@ pages. And finally the shame of exposure when I fatally carried them home wrapped in my purple coat on a windy day. I didn’t make it past the crossing guard….Thank you Mrs. Crawford…I never got in trouble for all this. I DID learn how to add and that the phrase “It’s just new math” meant it was okay not to understand it.

[michaelhelperin]

I was in elementary school in the 70's and had the great good fortune to be instructed in both New Math and traditional mathematics. I understood and loved the "enrichment mathematics" topics of Set Theory, Base Eight, and Modular Arithmetic and even today feel they stood me in good stead as a math tutor, but I doubt I could have grasped them without also learning my times tables! The two approaches complement and build on each other. As the graphitti in the library put is, "Facts without theory are chaos; theory without facts is fantasy."

[AcmeRacing]

I got the "New Math" version with set theory in first through third grade, which would have been fall 1971 through spring of 1974. The next year we went to the old-style algorithms for things like long division, and set theory was gone until I started Algebra in seventh grade. (I learned long division the alternate way the kid is doing it at 36:36.) It was difficult at first, but it made much more sense once I mastered the "real" algorithms. When my nieces got common-core and the "whole language" approach for English, I shook my head and told them about the education fad I had endured. I've tutored math as an adult, and I always start with a real-world example and then show students the equation, related back to the example so they can see why it works as it does. For compound interest, I'd do a simple problem for two or three compounding periods and _then_ show them the formula with exponents. (Even algebra and geometry are easier to comprehend with practical applications thrown in.)

[runningwitscissrs]

I was going through my subscriptions the other day and unsubscribing from things I didn't watch anymore and channels that weren't uploading anymore but I didn't unsub from this one. So glad! Amazing as usual! You keep making things and I'll keep watching :)

[dansman]

First off, let me say that I appreciate your honesty in posting a transcript for this video. It shows you prioritize accessibility over view maximization. I'm not the type to watch these videos since reading is usually more efficient for me. I say "efficient" since most video essays do not have ideas that are that dense, so there is no benefit engaging with them in a slowed video format. Note that this does not mean the video was bad, in fact I think it was rather good based off of the transcript. I just mean not "dense" as in comparison to, say, the definitions and proofs of a math textbook. One of my biggest issues a few years ago was that I would watch video essays in high school and get bored halfway through. Subtitles would help, but they were only ever a partial fix since I would have to use the left/right 5 second shift buttons to skip over uninteresting bits. These would usually be historical context, since that stuff tends to overlap the most among video essays which talk about the causes and context of events in the past. Reading at my own pace is much better since when things are written, you can find the novel bits quite literally "at a glance". These minor gripes aside, I learned some genuinely interesting things about the "new math" program! I think it's particularly interesting that the reform was spearheaded by a gifted education teacher; I think one of the best things about those classes is that they treat students in a way where they have faith in their natural capacities to learn and figure out new things, instead of treating them like animals to be trained/disciplined (which has the side effect of "neutering" spontaneous behavior, to make them easier to behaviorally "manage") . The human mind is incredibly malleable, especially at a young age. Honestly, the vast majority of kids are capable of the level of self-directed learning reserved for "gifted" schools, and I think it's an awful shame that most kids are corralled into classes that stamp out their natural sense of curiosity. Even worse that the careful visions of people like Beberman were defamed by the botched elementary-level new-math.

I would have liked more coverage of the details of Piaget's theory, and how specifically they were used to justify the premature imposition of elementary-school "new math". I also think there's more to explore on the causes of the disconnect between industry-written "school math" textbooks (who often get completely unrelated professors to attach their names to conglomerated rehashes of franken-textbooks as "authors") and the art of "math" itself. I think the fact that some husk-like remnants of New Math remain in the curriculum (like the unmotivated terminology of the "commutative law of addition" at the elementary level) speaks more to the laziness of K-12 textbook industries competing to cut costs by rehashing definitions without regard for a proper context to motivate them, and less to the lasting effect of New Math. I could be wrong on this last point though; it'd help to have some specific examples of high school New Math as it appeared back then and examples of the bits that persisted.


PS: The professor you interviewed was great! I'm sure he's likely got more details in the book he's written.
"The one thing mathematicians would say is, 'why would I calculate?' That's not interesting at all!" Love that guy

[lovealwaysmanish]

Dude you make these outstanding videos, highly underrated btw and upload them for free then dissappear for a while out of the blue, It's beyond my understanding. Anyways, great video about a topic I don't know shit about yet was still intrigued af

[rosameltrozo]

I didn't know i was subbed to this channel, but i'm glad now.
As for new math, well, it is quite sad that good ideas fail miserably due to lackluster execution.

[vandazandlova]

not me looking at the new math chalkboards and thinking "why didn't they teach us that at elementary school? it would have been so much easier than to having to figure it out myself on the fly mid-high school!"

[sorendont]

this editing is really "Voxxy", i like it quite a lot

[tomrobla]

I suffered through SMSG math in the 1960s. The SMSG textbooks were still in draft form. It wasn't until I took an advanced college mathematics course in Abstract Algebra that I understood what they were trying to teach. Important concepts for mathematicians to understand but not little kids.

[karstenmahlzahn]

Great Video! Epic Editing and Storytelling :D

[HaramGuys]

I have a masters in pure mathematics. Abstraction should always come after plenty of concrete examples as a way to connect the dots and form patterns. Never start with the abstract

[stuffofmaking]

This is by far one of the highest quality videos I've seen on YouTube for a while! Same feeling I have every time you upload honestly. :)

Also as someone who's right now working towards a master in math and considering entering math education at some point this had some great insights. Even though I don't live in the US many core concepts and ideas I believe are the same anywhere in the world.

Personally I fall mainly in what might be considered a third category on how math could be taught, and that is through "non-standard" problem solving. Of course you might need some solid computation and theory to have a toolset to begin with. But a general skill of problem solving can be done with theoretically and computationally easy tasks, and is something almost impossible to just pick up through reading and even understanding. Much like writing and analysing a good text vs writing one. I also strongly believe that by creating interesting problem sets you can easily introduce certain theory by having the students themselves create it, followed only later by a more thorough review of it. This would not only give a sense of exploration, but also solidify some core concepts which may otherwise be glanced over quite passively. At least at the level we expect the general middle/high schooler to be at. It would be a limited approach in some regards and require a lot of teachers to approach things differently, but a happy middle ground of everything is always best.

[eyeeye]

Have been watching since moments in time. You’re gonna be big I swear.

[therunt]

I think it's exactly what I needed, I adore and understand concepts and I NEED to know them in order to care about the mechanical equation part. I learn from the top down!
I think when I was in school in the 70s and 80s there were some teachers and schools that taught this way and some that didn't, and my mom moved a lot so I changed schools almost every year on my mom's whim. I definitely did better when a math teacher humored me enough to answer my questions about why and what for.

[PyroMancerk]

The biggest problem with pubic education is the complaint that people mention in their protest against New Math, You got people on high coming in and demanding things be done their way. There is no one size fits all solution. Different communities have different needs and might learn better with different curriculum. But instead they want to put a one size fits all approach.

For all the talk of how US schools are falling behind European schools they refuse to do the most important thing of all. Give Parents FREEDOM OF CHOICE. Instead they lot students into schools based on where they live which ensures poor in poor neighborhoods end up with poorer schools since schools are funded by local taxes dollars. In Europe parents can pick which local school they want to send their kids to, often referred to as Charter Schools here in the US were they do occur.

Most people can't afford to move in they find out their school is lacking and are stuck begging the government to improve things. But with the ability to choose parents will pull their students from failing schools and put them in ones that do have successful curriculum. Schools get paid per student by the government so it's still publicly funded the only difference is that now schools actually have to do a good job or else the parents will pull their students and that school will get closed down as it should be. Then if New Math, Common Core, or any of the other ideas actually do work the results will speak for themselves, otherwise they will get dropped like every other bad idea.

[russellbanks]

Love this, the editing and story telling is amazing.